Half-term, and the streets of central London are a scrabble of teenage boys, skateboards tied to their backs, acne loose all over their cheeks. Twenty five years ago a sight of the real Debbie Harry, poster-girl made incarnate, would have dropped these teenage boys to their knees. But 25 years ago, these particular teenage boys weren't born.

"I was out earlier and I just had my little sweater and some shades on," says Harry, "and I'm just walking around. And then I realised it was a little cold so I put my hood up. I looked like the Unabomber, right? Huh." Her laugh comes out in one go, like someone being hit in the stomach. "I guess I wasn't recognised. I guess I got away with it."

Back home in Chelsea, her neighbourhood in New York, there are people she sees every day who don't know who she is - who she was. "Most of the time, we know each other's dogs' names but not our own," she says. You mean it's a kind of dog thing? "Absolutely," says the owner of Chi-Chen, a pug, and Ki-Suki, a Japanese spaniel. "Absolutely."

But truly, you couldn't not recognise Deborah Harry (as, grown-ups all together, we now call her). You'd have not to know her face in the first place. She is 58 and fashion fascists Trinny and Susannah would have her out of those loose black leggings - a bit baggy around the bottom, a bit Florida retiree - and into something more tailored before you could say "Rip her to Shreds". The T-shirt with its acid-green stripe would go (trying too hard). And the leopardskin boots? Very Theresa May. (She learns May is the Conservative party chairwoman who wore leopardskin shoes to this year's conference and says, "Oh, and they all thought she'd gone mad, right? She'd gone wild?")

Harry is shorter and rounder than one might remember, and the harshly dyed mop of hair is these days more brittle than lush, but the face is still remarkable: the sleepy, slitted pale eyes in their cavernous sockets; the outsize Andy Warhol mouth - the cheekbones so angular they seem to have come from another part of the body altogether, like the hip. She is in London to promote a Blondie reunion tour and a greatest hits CD, holed up, after her little walk, in a suite in the unspeakably cool St Martin's Lane Hotel. White walls, black clothes, white hair: like the monochrome cover of 1979's Parallel Lines.

At their height, before they fell apart in 1983, Blondie were the ultimate new wave band. They were the acceptable face of punk - punk with a pretty face and a catchy commercial edge. Harry was in her 30s even then. She had a past: she had been a Playboy bunny, worked as a waitress, serving Janis Joplin down in Greenwich Village, hanging out with Patti Smith and Nancy Spungeon. She was even in a long-term relationship, with Blondie's guitarist and co-composer Chris Stein. But none of this stopped her playing rock star to the max. There was drink and drugs and outfits stuck together with duct tape. There were hotel rooms bashed up. "Yeah, absolutely. We were bashing dressing rooms, hotels, bashing each other. Why? I don't know. Zeal?"

It is an uncomfortable business interviewing a former pop icon. Harry is half rock-chick, half-granny. She pours you water, worries at the thinness of your sweater. She says "little" a lot (as in, "Oh, my little bag with its cute little badges."), is endowed with the occasionally pouting conversational tweeness of the childless, animal-doting older woman. Her voice can be Monroe-soft and cooing. She darts out her tongue to lick the top of her lip. She looks at you, kittenish, from under her lashes. She has self-deprecation on tap: "I've made nothing but mistakes."; "Which bad period? I've had quite a few."

But there is a nervy fluster about her assistant when her lunch is being ordered. And when the door goes and no one jumps to it, Harry pulls herself up to full icon height and yells: "THE DOORBELL. SOMEBODY'S KNOCKING." If a question implies she is staging a comeback; the answer assumes she has never been away. She doesn't like to talk of herself as a pop star (past glories), so much as a conceptual artist, an artiste (ongoing).

She was adopted by a couple in New Jersey. Her father was a salesman; her sister runs an American Italian restaurant. But her birth mother was a concert pianist. "It's genetic," she says. "I was always going to be an artist, in one field or another, come hell or high water."

And fields she has crossed. After Blondie collapsed, Stein became ill with pemphigus, a near-fatal skin disease and she looked after him for three years. They split up shortly after he recovered. (He married; she has had "some intimacies".) There were three solo albums for her, and, subsequently, appearances on stage and in film, and an ongoing relationship with the band Jazz Passengers.

But it has never been the same. There are tabloid stories about hair loss and weight gain, and "those bitches", as she once jokingly said, wearing the trash-blonde crown - Madonna, for one. "I don't think I will ever have the kind of celebrity that J-Lo has or Madonna," she says, "because they really don't have any privacy." (Interesting that "I will ever", keeping the possibility open.)

She did a photo shoot for Vanity Fair's music issue recently. She is in a line-up that includes Gwen Stefani, Sheryl Crow and J-Lo (J-Lo was the only one allowed an entourage: she had three bodyguards). What was the attitude of the younger singers to her? "We were all stars star-struck with each other," she answers firmly. Is the new Blondie audience a sea of pogo-ing middle-aged men? She doesn't smile. "Blondie has always had a wide age range." But then I tell her about someone I know who, as a teenager, had her picture on his wall and convinced himself her dress was getting shorter. She roars with laughter. She falls sideways on the white sofa like a tree being felled. "Oh, the old getting-shorter-dress in the poster trick," she hoots. "Yeah! He's seeing if he can see under it! That's cool!"

The story seems to untap something. After that, she talks about how she didn't appreciate the adulation at the time. "I just sort of wandered into it. I was very wooden when I started. I really didn't like the way I looked and I was all nghhg -" she twists her shoulder sideways - "all kind of creeped out. And self-conscious." She remembers meeting Joe Strummer on a radio show. "He was so ... so ... I loved him." If it hadn't been for Stein, you could have been the Mrs Strummer. "One never knows, does one?"

She recounts the day she first spent some serious money. "The first thing I bought: it cost $300. It was a beautiful coat by Yohji [Yamamoto]. It was a cotton-quilted, square thing, with these big square pockets. Like a tunic. I bought it at Henry Bendel's when it used to be on 57th Street and I was so panicked by the time I got it home, I was ready to just die." She gives a slanted look. "I quickly learned to get over it. I will succumb."

She moves on to therapy ("I love my therapist. She gives me tools. Visualisation.") and her apartment ("It's in transition right now. It's very eclectic, it doesn't speak of any one period or style of furniture, and I'm honing it.") and the rings on her fingers (each one has a story, each one a "find", though they are bothering her at the moment, she thinks she might have "a little case of hives"). Actually, she hates her hands. "I think they're awful. They are sort of large hands which I've always sort of regretted."

She has had a little facelift - "Oh, years ago now," - and pulls in the corners of her jaw to show me. "It's holding up," she says. She has tried Botox. "But I don't like the frozen look. I like to have expression. I have lines. I guess when I start to really need it, I'll do it again." In the meantime, she believes in exfoliation. "I think exfoliation is a wonderful thing," she says. "If you're aware of it, you should do it."

And I think she could have talked another hour about her cat, Peach, and her two dogs. Harry got the first dog to keep her company on tour, but it turns out she gets nervous in a strange environment, so that turned out to be impractical. But she rides in a basket in the front of Harry's bike: "With her long ears streaming out, looks very elegant." And the other one? "The other one's got to stay home, the other one's wild, the other one's much more doggy than the old dog. It's a constant battle. But I'm hooked. It's so easy to fall in love with a puppy, it's frightening. It's like, ooh, ooh, ooh." She makes a noise like a little orgasm. There is a slightly embarrassing pause after that.

Does she ever wish her life had been different? She gives a hefty sigh. "I don't know. You have a bad day, what do you think? I could be just playing golf somewhere or playing bridge with the girls. But I've done this. This is who I am."

· Blondie: Greatest Hits is out now. Their tour starts on December 5 in Glasgow.